We consider the fractional Heston model originally proposed by Comte, Coutin and Renault [12]. Inspired by recent groundbreaking work on rough volatility [2, 6, 24, 26] which showed that models with volatility driven by fractional Brownian motion with short memory allows for better calibration of the volatility surface and more robust estimation of time series of historical volatility, we provide a characterisation of the short-and long-maturity asymptotics of the implied volatility smile. Our analysis reveals that the short-memory property precisely provides a jump-type behaviour of the smile for short maturities, thereby fixing the well-known standard inability of classical stochastic volatility models to fit the short-end of the volatility smile.

PurposeThe purpose of the study is to examine overreaction effect in the Chinese stock market after the global financial crisis (GFC) of 2007 for all the stocks listed in Shanghai Stock Exchange (SSE) Composite 50 index.Design/methodology/approachTo capture overreaction effect in the stock listed at SSE 50 Index, a time series analysis of average cumulative abnormal return within a unified framework is applied for the period of January 2009 to December 2015. From these loser and winner portfolios, contrarian strategy is applied to build arbitrage portfolio, which is the difference of mean reversions between loser and winner portfolios. The portfolio construction is based on a 12-month formation period and 6-month testing period for intermediate-term analysis and. for short-term analysis, 6 month formation and 3 month testing periods. The authors also applied regression analysis to test a return reversal effect for the sampled period.FindingsResults show that contrarian strategy yields positive excess returns for the arbitrage portfolio for most of the testing periods. The intermediate baseline case shows the arbitrage portfolio producing an average excess return of 14.1%, while even the short-term one produces 4%, which is statistically significant at the 5% level. The study finds asymmetrical overreactions in the SSE especially for loser portfolios. The biggest winner and loser portfolios follow the mean reversal effect. Moreover, before-after test for the biggest winner and loser portfolios shows that the losers recovered and beat the market immediately.Practical implicationsThe study could benefit government, policy makers and regulators by studying how presence of more individual investors than institutional investors of China stock market leads to more irrational decisions giving rise to volatility. The regulators could build favourable policies for institutional investors to give them incentive to invest more than individual investors through which market volatility could be controlled.Originality/valueThis research contributes to market behaviour research, showing how working under hypotheses of overreaction; gains can be made with contrarian investment strategy through arbitrage portfolios. The authors provide specific additional support for the short and medium-term overreaction in the SSE for the period 2009–2015 using regression analysis.Contribution to ImpactThis research contributes to market behaviour research, showing how working under hypotheses of overreaction; gains can be made with contrarian investment strategy through arbitrage portfolios. We provide specific additional support for the short and medium-term overreaction in the SSE for the period 2009–2015 using regression analysis.

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We propose a randomised version of the Heston model-a widely used stochastic volatility model in mathematical finance-assuming that the starting point of the variance process is a random variable. In such a system, we study the small-and large-time behaviours of the implied volatility, and show that the proposed randomisation generates a short-maturity smile much steeper ('with explosion') than in the standard Heston model, thereby palliating the deficiency of classical stochastic volatility models in short time. We precisely quantify the speed of explosion of the smile for short maturities in terms of the right tail of the initial distribution, and in particular show that an explosion rate of t γ (γ ∈ [0, 1/2]) for the squared implied volatility-as observed on market data-can be obtained by a suitable choice of randomisation. The proofs are based on large deviations techniques and the theory of regular variations.